Sven and DP are only good for pushing 1 lane at a time (2 at most). Early game Sven doesn't amount too much and late game pushing is high-risk since he is the carry. DP is mostly just for crowd control while ult is down.

Tinker is not an all-around pusher and is easily countered (wards bro). I have no idea why Slark is here. Out of the list, the only logical choices are NP, Invo, and SF. But if its my personal choice, I'd say: Geo (3 lanes at once, while defending, while jungling,without any high-risk), Arc Warden (come on dude, he can stay at the well while pushing), and Nature's Prophet.